Can someone help me with this rotational dynamics problem.

1. The problem statement, all variables and given/known data
I've been trying to attempt this problem for the past day but I don't understand how to answer the questions. It's frustrating. If someone could point me in the right direction that would be nice. My TA did the problem in class but I still don't quite understand it. This is my first time taking a physics course.

A plank with a mass M = 5.60 kg rides on top of two identical, solid, cylindrical rollers that have R = 4.40 cm and m = 2.00 kg. The plank is pulled by a constant horizontal force of magnitude 6.40 N applied to the end of the plank and perpendicular to the axes of the cylinders (which are parallel). The cylinders roll without slipping on a flat surface. There is also no slipping between the cylinders and the plank.

(a) Find the initial acceleration of the plank at the moment the rollers are equidistant from the ends of the plank.
magnitude: m/s2
direction:

(b) Find the acceleration of the rollers at this moment.
magnitude: m/s2
direction:

(c) What friction forces are acting at this moment? (Let fp be the frictional force exerted by each roller on the plank, and let fg be the rolling friction exerted by the ground on each roller.)
fp = N
direction:

A plank with a mass M = 5.60 kg rides on top of two identical, solid, cylindrical rollers that have R = 4.40 cm and m = 2.00 kg. The plank is pulled by a constant horizontal force of magnitude 6.40 N applied to the end of the plank and perpendicular to the axes of the cylinders (which are parallel). The cylinders roll without slipping on a flat surface. There is also no slipping between the cylinders and the plank.

(a) Find the initial acceleration of the plank at the moment the rollers are equidistant from the ends of the plank.

try (a) first …

start by giving things names: call the acceleration of the plank "a", the angular acceleration of the cylinders "α", and the friction force between the plank and each cylinder "C"

write out the F = ma equation for the plank, and the τ = Iα equation for each cylinder, and also the "rolling constraint" equation that relates a to α …

Then set that equal to my Torque function and solve for C? Then I can plug that into my a) equation to find the acceleration?

yes , but …

Torque is Radius x Force so would it be Radius x 6.4-C?

i] the 6.4N is not a force on the cylinders, so it does not contribute to the torque
ii] the friction with the ground does contribute to the torque
iii] you don't want to have to find the friction, so about which point should you measure the torque?

But the 6.4N is the cause for the rotation of the wheels which is parallel to the cylinders. If there were no 6.4 N they wouldn't rotate. The only other force I can think of that is applied to the cylinder is the downward force of mg on from the plank. Is friction the only force that contributes to the torque? Excuse my ignorance, I'm trying every opportunity I see.

F_p is to the right on the top of the cylinder and F_g is pointing to the right on the ground. I got that but how do I go about finding the initial acceleration when the rollers are equidistant to the ends of the plank. I'm lost in the abyss .

F_p is to the right on the top of the cylinder and F_g is pointing to the right on the ground. I got that but how do I go about finding the initial acceleration when the rollers are equidistant to the ends of the plank. I'm lost in the abyss .

fp acting on the cylinder is to the left if the cylinder is being pulled to the right.

The cylinder will exert a force of fp on the ground which is to the right.

F_p is to the right on the top of the cylinder and F_g is pointing to the right on the ground. I got that but how do I go about finding the initial acceleration when the rollers are equidistant to the ends of the plank.

the only significance of the "equidistant" thing is that it means that the normal forces are the same, and so the friction forces are also the same

(it just makes the arithmetic easier! )

ok, you now have a free body diagram which tells you there are only two forces that can give a torque to each cylinder: the plank friction force (Fp), and the ground friction force

you have a completely free choice as to which point you take torques about …